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Adaptive cyclic gradient methods with interpolation

Author

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  • Yixin Xie

    (Beijing University of Posts and Telecommunications (BUPT)
    Key Laboratory of Mathematics and Information Networks (BUPT) Ministry of Education)

  • Cong Sun

    (Beijing University of Posts and Telecommunications (BUPT)
    Key Laboratory of Mathematics and Information Networks (BUPT) Ministry of Education)

  • Ya-Xiang Yuan

    (Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences)

Abstract

Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values.

Suggested Citation

  • Yixin Xie & Cong Sun & Ya-Xiang Yuan, 2025. "Adaptive cyclic gradient methods with interpolation," Computational Optimization and Applications, Springer, vol. 92(1), pages 301-325, September.
    • Handle: RePEc:spr:coopap:v:92:y:2025:i:1:d:10.1007_s10589-025-00691-y
    DOI: 10.1007/s10589-025-00691-y
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    References listed on IDEAS

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    1. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
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    4. Roberto Andreani & Marcos Raydan, 2021. "Properties of the delayed weighted gradient method," Computational Optimization and Applications, Springer, vol. 78(1), pages 167-180, January.
    5. di Serafino, Daniela & Toraldo, Gerardo & Viola, Marco, 2021. "Using gradient directions to get global convergence of Newton-type methods," Applied Mathematics and Computation, Elsevier, vol. 409(C).
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